By Lina Sorg
Quantitative radiography is an imaging technique that uses electromagnetic radiation, such as X-rays, to gather quantitative data about the interior of nontransparent objects that vary in density and composition. For example, radiography is particularly helpful when reconstructing objects composed of multiple materials, such as different types of metal. In order to generate these images, most high-energy technologies pulse X-rays through the “scene” in question; objects in the scene absorb some of the rays, while a scintillator – which measures the strength of the passing X-rays – collects the rest and fluoresces (emits visible light) in response to the collected rays. Possible scenes include parts of the human body, thermal explosions, nuclear testing sites, and other applications of national security. The resulting images directly measure the intensity of visible light, yielding information about the objects’ internal structure.
In a paper recently published in the SIAM Journal on Scientific Computing, authors Marylesa Howard, Michael Fowler, Aaron Luttman, Stephen Mitchell, and Margaret Hock propose a new statistical formulation that provides a more precise estimate of the densities of objects imaged by the aforementioned X-ray techniques. They utilize data from the Cygnus Dual Beam Radiography facility at the Nevada National Security Site.
Howard et al. use a variational Gaussian noise model that places Abel inversion, an integral transform frequently used in image processing, within a statistical framework. This placement permits the authors to compute object densities and quantify uncertainties during image reconstruction. The authors then create a hierarchical Bayesian model with priors placed on unknown density profiles. Such positioning allows the model to simultaneously estimate the densities of objects as well as the locations of density discontinuities, which occur when objects are comprised of different materials. From this information, the authors obtain estimates of both the uncertainties in the reconstructed densities and the sites of these uncertainties.
The average reconstruction resulting from the authors’ techniques outperforms existing imaging regularization methods, thus rendering more accurate images and densities. These improvements could positively impact radiography’s use in various applications of national security.
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Source article: Bayesian Abel Inversion in Quantitative X-Ray Radiography. SIAM Journal on Scientific Computing, 38(3), B396-B413. (Online publish date: May 19, 2016).
About the authors: Marylesa Howard, Aaron Luttman, and Stephen Mitchell are scientists/mathematicians at National Security Technologies, LLC, in Las Vegas, Nevada. Michael Fowler is an applied mathematician at MathWorks, Inc. Margaret Hock is an applied mathematics and statistics student at the University of Alabama in Huntsville.
||Lina Sorg is the associate editor of SIAM News.